That rumbling? That’s the sound of thousands of teenage girls flocking to NYC. Baby-faced teen idol Justin Bieber will be recording his next album in the city. In papers filed in Manhattan Supreme Court, Bieber’s record label, Universal, seeks a judge’s permission to get its latest contract with the singing sensation approved. (He’s a minor, so a judge has to make sure no one takes advantage of him.) Bieber, 16, signed the two-record publishing deal in December and is getting a $400,000 advance on the first CD, The Post’s Dareh Gregorian reports. Bieber is “providing his services as a recording artist in recording studios located in New York City,” the filing says. Universal also tells the judge not to worry — “the foregoing services rendered by the minor shall not, however, require excessive time as to interfere with the minor’s education and welfare.” Priorities!